TP 1 Fonctions récursives - Alain Camanes

n n
x∈Rn∈Nxn
x0= 1 xn=x·xn−1n > 1.
−
•plus petits
•cas de base 0
récursifs
1. !
2.
3.
4. a)
<
b) π10−10

5. Exponentiation rapide. x n y =xbn
2c
x0= 1,
xn=y·y n ,
=x·y·y n .
a)
b2c
-b) T
= (bt···b0)22
i. //2 %2
ii. log2( )
iii. T(bt···b0)2=T(bt···b1)2+b0+ 1
iv.
6. Plus grand diviseur commun. a b a >b r
a b a b a ∧b
a∧0 = a a ∧b=b∧r.
a)
-b)
1844
7. Fibonacci
F0=F1= 1, Fn+2 =Fn+1 +Fn,∀n∈N.
a) F
b) F
c) F35
-d) T
T→+∞
e)
8. Tours de Hanoï.
a)
-b)